I can attest to leaving the fridge open. Forgot to do that twice. It doesn't take long for it to get nasty!
I store mine.....usually maybe 4-6 weeks at the most between trips. Few times longer
I strongly considered a solar trickle charger. I have bought too many batteries in boats and my old popup camper, learning about self discharge.
They'll loose roughly 5% charge per month with noting connected.
Going for a moment with the common rule of thumb to never let them go below 50% capacity, that means a fully charged battery might last about 10 months in storage. Considering that it may not be full to start with, and it may drop a bit more than 5% in a month, and probably other variables too, I wouldn't want to stretch close to that number.....but I figured if it's stored for 2-3 months at the most things should be ok without charging
But
I want to make sure I'm only loosing from self discharge and that there's no other parasitic loads
so the first thing I did to my MH was add cut-off disconnect switches to both my chassis and house battery. Whenever I park to store, even for a short while, I'll disconnect them. I didn't end up going with any sort of trickle charger and have not so far had a problem. I'm on 3 years now with the cheap hybrid battery that camping world provided. It's showing signs of reduced capacity now, but I had some issues that caused me to deep discharge teh thing a couple times so it's expected. (BIRD relay failed for one so the battery didn't charge)
The other things I do
reflectix in all the windows
insulating pillows in the roof vents
stabilizer in my gas when storing
and my new thing since having a blowout is cover my tires